x264: no, but framerate isn't a codec-level problem at all. (Even if the elementary stream technically has a framerate.) Look in the containers forum for advice on doing that, search for VFR or Variable framerate. There are a number of tools to do it in MKV, MP4, or MPG, especially when you use avisynth. (Maybe TS by now.)

__________________There are four boxes to be used in defense of liberty: soap, ballot, jury, and ammo. Please use in that order. ~ Ed Howdershelt

x264: no, but framerate isn't a codec-level problem at all. (Even if the elementary stream technically has a framerate.) Look in the containers forum for advice on doing that, search for VFR or Variable framerate. There are a number of tools to do it in MKV, MP4, or MPG, especially when you use avisynth. (Maybe TS by now.)

Thanks for the info mate.

TS? As in "Thread Starter"? I'm not quite understand. Sorry for my English.

Do not use variable framerate! This is after doing some video editing in Adobe Premiere and having to work with some variable framerate recorded videos. The videos play back fine in players because there are contingencies for this type of video. But in video editors like Adobe Premiere, you have a good chance of getting audio/video sync problems. And these problems are driving me mad.

Does anyone have an easy solution for converting variable framerate videos without losing quality so that I can use these videos in Adobe Premiere?

fpsnum and fpsden need to be set according to the target frame rate. Note that 100% lossless conversion from VFR to CFR is not possible except for a common multiple (e.g. 120 fps CFR for 24 fps and 30 fps hybrid VFR).

I believe VFR should be very useful for content types like animation, where real framerate might be 2-3 times lower than the nominal one. Or for hybrid content, combining 25 and 30 fps videos, so that there will be no need to use 120fps videos like people used to do for a while already.
You might want to take a look at Dup and DeDup filters of Avisynth, they are supposed to generate timecodes file to convert CFR to VFR.

I believe VFR should be very useful for content types like animation, where real framerate might be 2-3 times lower than the nominal one. Or for hybrid content, combining 25 and 30 fps videos, so that there will be no need to use 120fps videos like people used to do for a while already.
You might want to take a look at Dup and DeDup filters of Avisynth, they are supposed to generate timecodes file to convert CFR to VFR.

That's a very bad idea especially for modern animation. Nowadays there is no animation that might have real framerate lower than 24fps (unless this is some doujin stuff). Most of the time it can only be valid for foreground moving objects but bg is full 24fps.
This is also one of the reasons why things like Dup and DeDup should never be used. They are decimating frames based on pure guesswork and never accurate. Since such algorithms are never perfect and frames in animation can look very similar, you'll end up with some good frames missing, which makes things less smooth. Unless you'll tune the decimation algorithm to be very careful and thus not only practically useless but theoretically too. And even regardless of that, streams where fps jumps like hell from one to another is a pain in the ass for renderers, which also works against smooth playback.
Modern formats such as h264 already handle things like duplicated frames or parts of the frame internally quite well.
On the other hand no one stops you from creating hybrid content with, for example, most of the stuff 24fps but portions with 30 fps, and never did. 120 fps with dropframes was used only to achieve the same effect with obsolete formats.